This project continues the development of clinical trial design and statistical analysis methodology for psychopharmacological and other treatments used in the care of the mentally ill. The specific aims are to: (1) develop design and statistical analysis strategies for dose-response and bioassay studies to characterize a test treatment relative to a standard treatment. Based on models that include patients who are unresponsive at any dose, who respond at any dose or who respond depending on whether their dose is adequate, we will develop methods to analyze "doctor's choice" study designs. Recursive partitioning approaches for identifying variables that share a common relative potency will be studied. (2) develop clinical trial designs and methods of analysis resulting in clinically informative measures. We will develop an inference framework for optimal scaling techniques for the general linear model and for two-way tables when the data arise from ordered categories. We will develop efficient designs and nonparametric and parametric models and estimators of parameters that are clinically informative. (3) develop simple designs and statistical methods for testing whether each component of a combination therapy contributes to its effect and whether the combination is antagonistic, additive or synergistic. In the multivariate combination problem, we will study new hypothesis formulations that further characterize the requirement that each component "contributes" to the combination's effects. Alternatives that are more demanding than admissible but less demanding than uniformly best will be developed. We will study the problem of finding a simple experimental design to test for dose additivity, synergy or antagonism when there are two or more doses of the combination, single and multiple endpoints and combinations with two or more drugs. (4) develop robust and optimal crossover and response adaptive clinical trial designs for estimation of treatment and carryover effects. We shall seek optimal crossover designs for an arbitrary number of treatments and periods when there are carryover effects. We will develop response adaptive designs to allocate treatments to patients so as to increase power for hypotheses testing situations involving a min statistic and in the optimal crossover design problem.